Ehrlich occupancy time: Beyond k off to a complete residence time framework

bioRxiv (Cold Spring Harbor Laboratory)

Abstract

Abstract Drug-target occupancy time—the cumulative duration a target remains bound—critically influences therapeutic efficacy. While Copeland’s widely-used residence time (1 /k off ) emphasizes dissociation kinetics, it neglects association rates, rebinding events, and drug elimination that affect in vivo outcomes. Returning to Paul Ehrlich’s 1913 principle that drugs act only when bound (“Corpora non agunt nisi fixata”), we develop a mathematically rigorous framework defining Ehrlich occupancy time, EOT, as the integral of fractional target occupancy over time. Our approach explicitly incorporates association ( k on ) and dissociation ( k off ) kinetics, accounts for rebinding, and extends to systems with drug removal. For drug-receptor closed systems at equilibrium, we prove that relative EOT equals the equilibrium occupancy fraction; under ligand-excess conditions this reduces to b 0 / ( K d + b 0 ), where K d is the dissociation constant and b 0 the drug concentration. For induced-fit mechanisms, conformational changes reduce the effective dissociation constant to (where k 3 and k 4 are forward and reverse isomerization rates), prolonging occupancy through kinetic trapping. Critically, for drug-receptor systems with firstorder drug elimination at rate k 3 , we derive rigorous bounds: b 0 / [( b 0 + K d ) k 3 ] ≤ EOT ∞ ≤ b 0 / ( K d · k 3 ), where EOT ∞ := lim T →∞ EOT( T ) is the total cumulative occupancy time as T → ∞, revealing that both binding affinity and elimination rate jointly determine occupancy. This explains why high-affinity drugs can fail clinically if eliminated rapidly, and identifies pharmacokinetic optimization opportunities. We prove Copeland’s definition is a special case of Ehrlich occupancy time when rebinding is absent. Our framework provides quantitative tools for optimizing drug design beyond binding affinity and enables improved prediction of in vivo efficacy where pharmacokinetics dominate.

Authors 3

1. Justin Eilertsen

   American Mathematical Society

   Affiliation as printed

   Mathematical Reviews, American Mathematical Society, 416 4th Street, Ann Arbor, MI, 48103

   Mathematical Reviews, American Mathematical Society

2. Santiago D. Schnell corresponding

   Dartmouth College

   Affiliation as printed

   Department of Biochemistry & Cell Biology, Hanover, NH 03755

   Department of Biomedical Data Sciences, Geisel School of Medicine at Dartmouth, Hanover, NH 03755

   Department of Mathematics, Dartmouth, Hanover, NH 03755

   Dartmouth

3. Sebastian Walcher Aachen Fachgruppe Mathematik

   RWTH Aachen University

   Affiliation as printed

   Fachgruppe Mathematik, RWTH Aachen, D-52056 Aachen, Germany

   Fachgruppe Mathematik, RWTH Aachen